35,36 Mmpp loading models

Markovsky modulation of Poisson process (MMPP) represents dual Poisson process with the arriving speeds depending on phases (conditions) which make the Markovsky chain of continuous time. Modulation MMPP is a special case of process PH-MRP and, thanking its pliability (удобности), is widely used at modelling of raging streams of transport loading, such as the packaged speech signal in networks ATM. Stream MMPP can be analysed with use of a method of analytical matrixes.

On fig. 14 it is shown diphasic MMPP, as the most simple case having Poisson rate of receipt lj in a phase j, j = 1,2 which appears serially with экспоненциально distributed time of life with a population mean rj-1. It is characterised as (R, L) where R there is an infinitesimal generator of the Markovsky chain underlying, and L - a matrix of speed the receipts defined as formula (59)

System MMPP/G/1 model allows to define function of distribution of a virtual waiting time with use of the integrated equation of Voltaire. Study features of calculation of a virtual average waiting time and the valid (present) average waiting time.

System MMPP/Ek/1 model (m) is entered to approximate system MMPP/D/1 model (m), applied to analysis ATM of systems with constant length of a cell and with the size of the buffer m.

37 Statistical package multiplexer

In digital networks of integrated service ISDN loading multimedia on port, such as the voice, the data, video and etc., are transferred in the form of packages. In system of package switching of standard X.25, the package has variable length while in system ATM for broadband network ISDN the package becomes a cell of constant length. As the packaged process has in steps raging nature superposition process (imposed one on another) many sources becomes not pulsing. Therefore process MMPP was widely adopted at research of raging streams in networks of package switching.

The model of the packaged voice (video) is shown on fig. 15 as relay (ON-OFF model).

For a single sound source believe that the periods of the speech statement and silence are distributed экспоненциально with average sizes a-1 and b-1, accordingly, and packages (cells) are generated during T during the speech statement. From here define rate of receipt l, SCV Ca2 and asymmetry Sk.

Raging streams can be characterised indexes of a dispersion and asymmetry of number of the packages arriving for an interval of time (0, t]. Indexes are entered as the relation of the corresponding central moments to a population mean of arriving packages in time t. For dispersion and asymmetry indexes the law of preservation of indexes is carried out: indexes of an individual relay source are equal to corresponding indexes of superposition of process of receipt of packages from n independent sources.

The raging stream (from n independent sources) can be approximated superposition of packages diphasic process MMPP. Thus unknown parametres of process MMPP (rates of receipt of calls in different phases and distributions of time of life in different phases) are defined on the measured indexes of a dispersion and asymmetry of a raging stream.

The mixed models of raging loading of port from n independent sources approximate 2-phase process MMPP. We believe that superposition n individual 2-phase processes MMPPi forms mixed 2n-phase process MMPP which we approximate again diphasic process MMPP. Familiarise with model MMPP+M/G/1, study indicators of quality of the one-linear mixed system of service of the raging traffic (individual average waiting times on loadings MMPP and Poisson, accordingly; an average virtual waiting time of process MMPP in a phase l, l=1, 2; averages virtual and valid waiting times for the mixed loading with priority schemes; individual speed of loss of cells on loadings MMPP and Poisson, accordingly; virtual speed of loss of cells of process MMPP in a phase l, l=1, 2).

38-39 Local networks LANs

The go-ahead ring the Token Ring LAN is the standard report of type of consecutive management of access to services and services of the local computer network. In this report the signal of the permission of the transfer, named a marker, circulates between the knots placed on a contour of a ring. The knot having the data for transfer, carries out employment of the released marker and will transform it to the occupied marker which transfers a package of the data about its destination. After the package of the data has been accepted by the destination party, the marker comes back to the proceeding knot specified as generating party where it is released again and starts to circulate again on a circle. It is necessary to get acquainted with model of the "going" server, to be able to define structural parametres (average value and a dispersion of time of a course, employment of knot and server employment, time of a cycle and the general time of a course on a ring). Here it is necessary to give special attention to types of clearing of a marker and features of calculation of an indicator of quality of work (symmetric and asymmetric systems) go-ahead ring.

At calculation of an indicator of quality (an average waiting time for knot j) asymmetric (diverse conditions of transportation on knot) systems through course time the big expense of machine time is required. Therefore receive the formula of approximation of an average waiting time by introduction of time of vacation (a time interval between visitings of the same knot j) "the going" server.

Plural access with poll bearing and CSMA/CD LAN resolution of conflicts is the standard report of type of parallel management of access in the conditions of competitions on the general tyre of the local computer network. According to this report the knot having a package, transfers it after acknowledgement of an inactive condition of the general tyre, without having found out bearing on it. Thanks to a delay of distribution bearing, however, there is a conflict possibility. If it happens, clashing knots relay packages after predetermined time. Such procedure is called as operation (back-off) supports of the interrupted communication.

At calculation of an indicator of quality (an average waiting time for knot j) define the sum of average time of access thanks to the mechanism of management of access of CSMA/CD and a waiting time to turns on knot j type M/G/1. At calculation of last component the estimation of a population mean and the second moment of the first component for knot j is required.